Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #27161385 | C2 | semidirect |
| 4. #27161384 | C2 | semidirect |
| 5. #27161371 | C2 | semidirect |
| 6. #27161365 | C2 | semidirect |
| 7. #27161364 | C2 | semidirect |
| 11. #477×C197 | C2 | semidirect |
| 47. Q8×D197 | Q8 | semidirect |
| 130. C197 | #3078 | semidirect |
| 137. #477 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| C4×Q8×D197 | 2 |
| #27161385 | 2 |
| #27161384 | 2 |
| #27161371 | 2 |
| #27161365 | 2 |
| #27161364 | 2 |
| #27161120 | 2 |
| #27161101 | 2 |
| #27161086 | 2 |
| #477×C197 | 2 |
| #3078 | 197 |